| 15th October 2014 09:40 AM | |
| Arvind Kumar | Re: Integrated Ph.D entrance exam (Mathematical Science) syllabus This is the Indian Institute of Science Education and Research Integrated Ph.D entrance exam (Mathematical Science) syllabus: SYLLABUS 1. Algebra: Theory of Equations: Relation between roots and coefficients of an equation, Symmetric functions of roots, Rolle’s theorem, Reciprocal Equations, Descartes’ Rule of Signs, Cubic and quartic equations, Complex numbers and De Moivre’s Theorem. Determinants: Properties of determinants, Solution of a Linear System, Cramer’s Rule Inequalities: AM‐GM inequality, Cauchy‐Schwarz inequality. Set Theory: Relations, Functions, Bijections, Cardinality, Permutations and combinations of sets and multisets, Discrete probability. Algebraic Structures: Groups, Subgroups, Cosets, Normal subgroups, Symmetric group, Homomorphisms. Rings, Integral Domains, Ideals, Prime and Maximal Ideals, Polynomial Rings. Vector Spaces: Subspaces, Linear independence, Bases and dimension, Linear transform syllabus-1.jpg) syllabus-2.jpg) |
| 13th October 2014 05:33 PM | |
| Unregistered | Integrated Ph.D entrance exam (Mathematical Science) syllabus Can you provide me the Indian Institute of Science Education and Research Integrated Ph.D entrance exam (Mathematical Science) syllabus??????? |
